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Microbial communities often consist of many closely related strains or species that exhibit small genomic differences compared with one another. These variations are thought to play crucial roles in maintaining community resilience and in the evolution of new species. Multiple examples now exist for the impact of species and strain variations on community outcome and its environment as in the cases of methicillin resistant Staphylococcus aureus (MRSA) and pathogenic Escherichia coli. However, very little is known about the scale and dynamics of these variations in natural environments.
In this talk I will discuss species- and strain-variations in two distinct environments: the simple developing microbial community in the gut of newborns and the complex microbial communities in terrestrial sediments. Using new methods for the recovery of dozens of genomes from environmental DNA sequencing (metagenomics) data and an analysis of synthetic long reads we were able to thoroughly describe systems of species- and strain- variations in both environments. These include strain-specific phage predation during infant gut colonization, and also complex populations of dozens of species and strains in terrestrial sediments. The implications of our findings as well as future directions will also be presented.

I will discuss the recent application of the conformal bootstrap program to superconformal field theories (SCFTs) in 3d, focusing on maximally supersymmetric theories. In particular, the constraints from unitarity and crossing symmetry on the 4-point function of the stress-tensor multiplet can be implemented numerically, and lead to stringent bounds on OPE coefficients and operator dimensions. Moreover, in these SCFTs it is possible to derive relations between certain OPE coefficients analytically. These relations are obtained by restricting the operator algebra to the cohomology of a certain supercharge, and then solving the associativity constraints in the resulting truncated algebra. We will see that the numerical results are consistent with the above analytic relations. In addition, for the interacting SCFT that constitutes the IR limit of O(3) maximally supersymmetric Yang-Mills, the above constraints are powerful enough to allow for an explicit computation of 3-point functions of 1/2-BPS operators.